In memoriam Albert Verbeek (1946–1990)

Kroonenberg, Pieter M.

doi:10.1111/j.1467-9574.1992.tb01331.x

Statistica Neerlandica

1992

DOI: 10.1111/j.1467-9574.1992.tb01331.x

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In memoriam Albert Verbeek (1946–1990)

Pieter M. Kroonenberg

Abstract: ThisIn memoriam is divided into three parts. The first part is a tribute to AlbertVerbeek as a person and a scientist. In the second part, a short note is reproduced, translated from the Dutch, as an example how he applied himself to all kinds of problems. The final part consists of an overview of his major publications.

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1997

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“…14, In addition, as reported by most authors the convergence rate of the traditional PARAFAC algorithm is rather slow. 16,17 We recently developed an alternating trilinear decomposition method (ATLD) as an alternative method for decomposition of threeway data array. 18,19 It has been found that the ATLD algorithm proposed by us has a capability to converge the iterative process more rapidly than the traditional PARAFAC algorithm does.…”

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Second-Order Calibration Based on Alternating Trilinear Decomposition: A Comparison with the Traditional PARAFAC Algorithm.

Shibukawa

Oguma

1997

Anal. Sci.

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Quantitative analysis of p-chlorotoluene in the presence of o-chlorotoluene as an interferent was attempted by using HPLC with diode array detection and second-order calibration methods. An emphasis was placed on a further comparison between two methods, i.e., the traditional parallel factor analysis (PARAFAC) and the alternating trilinear decomposition (ATLD) methods. The following conclusions have been confirmed for the calibration examples tested. PARAFAC does not always converge to chemical meaningful solutions and its convergence rate is slow for the . This seems to be owing to the deficiency of a real trilinear sense in PARAFAC. The convergence rate of the ATLD algorithm is extremely fast. The ATLD-based calibration not only retains the advantage of second-order calibration but can give satisfactory concentration predictions.Keywords Second-order calibration, trilinear model, PARAFAC, alternating trilinear decomposition, singular value decomposition, Moore-Penrose inverse Second-order calibration has an advantage that quantitative analysis can be performed even in the presence of uncalibrated interfering species.'-9 Second-order calibration is usually performed by decomposition of a three-way data array and prediction of unknown concentrations based on regression of the relative concentration contributions of each component of interest in sample space against its standard concentrations. The three-way data array is composed of the responses from both the calibration samples and the unknown mixture samples. The typical methods are the direct trilinear decomposition (DTLD) 7, 8 and the PARAFAC algorithm.'0-17 However, theoretically, DTLD seems to be useful only when the cumulative percent variance of the first two principal components is close to 100% and otherwise other errors would be introduced because the number of factors in sample space is artificially restricted to two.The PARAFAC/CANDECOMP algorithm is only based on a series of the frontal slice matrices and includes both the three procedures of computing inverse matrices and the four addition procedures of a series of matrices containing plus or minus elements in each iterative cycle. Hence, the traditional PARAFAC algorithm is guaranteed to reduce the residual sum of squares at each iteration, but it does not always converge to chemical meaningful solutions. 14, In addition, as reported by most authors the convergence rate of the traditional PARAFAC algorithm is rather slow.16, 17 We recently developed an alternating trilinear decomposition method (ATLD) as an alternative method for decomposition of threeway data array. 18, 19 It has been found that the ATLD algorithm proposed by us has a capability to converge the iterative process more rapidly than the traditional PARAFAC algorithm does. The ATLD-based second-order calibration retains

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confidence: 99%

Second-Order Calibration Based on Alternating Trilinear Decomposition: A Comparison with the Traditional PARAFAC Algorithm.

Shibukawa

Oguma

1997

Anal. Sci.

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In memoriam Albert Verbeek (1946–1990)

Cited by 1 publication

References 10 publications

Second-Order Calibration Based on Alternating Trilinear Decomposition: A Comparison with the Traditional PARAFAC Algorithm.

Second-Order Calibration Based on Alternating Trilinear Decomposition: A Comparison with the Traditional PARAFAC Algorithm.

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